Zhijia Tan

Day-to-Day Flow Dynamics and Congestion Control

For a predetermined set of an upper bound of link flows, this paper proposes a price-based congestion control scheme for achieving such a restraint target of traffic flow that evolves from day to day. On each day, drivers have to pay a toll selected from a feasible set. The tolls on each day are determined by the link flows and toll charges on the previous day and the predetermined upper bound of link flows. Several properties of the dynamical system model with the control scheme are analyzed, including the invariance of its evolutionary trajectories; the equivalence between its stationary state and user equilibrium under toll charge; the uniqueness, existence, and boundedness of its stationary state; and the convergence of its evolutionary trajectories. A special case of the model and implementation of the control scheme for several alternative targets are also given. Finally, application of the model to a traffic network is demonstrated with a numerical example. The study is helpful for better understanding the mechanism of congestion control under day-to-day traffic flow dynamics.

Build-operate-transfer Schemes for Road Franchising with Road Deterioration and Maintenance Effects

Private provision of public roads through build-operate-transfer (BOT) approaches is increasing around the world. By considering both social welfare gain and profitability, the BOT problem is to determine the optimal BOT contract which can be viewed as a combination of three primary variables of concession period, road capacity and toll charge. This paper models the BOT problem as the isoperimetric problem in calculus of variations to maximize the social welfare with a profit constraint. The model explicitly incorporates the effect of road deterioration and maintenance over the years, which is assumed to depend on the traffic loads, road capacity and road natural deterioration. We find that an optimal pricing policy requires toll increase over calendar time to reduce traffic load due to time-increasing and load-increasing maintenance cost. If, however, the marginal user damage on road is independent of time, then the optimal toll charge is free from the effect of road natural deterioration and thus time-invariant. We also discuss how to reach an optimal contract through government regulations and investigate the effects of economic growth on the solution properties of the problem.

Modeling the Effects of Speed Limit, Acceleration, and Deceleration on Overall Delay and Traffic Emission at a Signalized Intersection

AbstractThis paper proposes a microscopic spatial-temporal method to capture the vehicle movement trajectories at an isolated intersection. A bi-objective programming model is presented to minimize...

Stability Issue of the Day-to-Day Link Flow Pattern with Heterogeneous Users

This paper studies the stability issues of the travelers day-to-day route adjustment process in the general transportation network with fixed or elastic demand, homogeneous or heterogeneous users. Each traveler is assumed to adjust his/her route choice according to the excess travel cost between the instantaneous experienced travel cost and a certain referred level, which induces an aggregate path flow dynamics. We call the path flow dynamics the excess travel cost dynamics, which corresponds to the excess payoff dynamics in evolutionary games and serves a general framework of modeling the homogeneous or heterogeneous route choice behavior of travelers.